%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:36:00 PM UTC 2026
% Result : Unsatisfiable 0.22s 5.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.48 % Computer : n026.cluster.edu
% 0.18/5.48 % Model : x86_64 x86_64
% 0.18/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.48 % Memory : 8046.5625MB
% 0.18/5.48 % OS : Linux 6.8.0-71-generic
% 0.18/5.48 % CPULimit : 300
% 0.18/5.48 % WCLimit : 300
% 0.18/5.48 % DateTime : Sun Sep 20 20:03:57 UTC 2026
% 0.18/5.48 % CPUTime :
% 0.18/5.49 % Drodi V4.1.1
% 0.22/5.52 % Refutation found
% 0.22/5.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/5.52 % SZS output start CNFRefutation for theBenchmark
% 0.22/5.52 fof(f1,axiom,(
% 0.22/5.52 group_element(e_1) ),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f2,axiom,(
% 0.22/5.52 group_element(e_2) ),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f3,axiom,(
% 0.22/5.52 ~ equalish(e_1,e_2) ),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f5,axiom,(
% 0.22/5.52 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2) ) ))),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f7,axiom,(
% 0.22/5.52 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f8,axiom,(
% 0.22/5.52 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f9,negated_conjecture,(
% 0.22/5.52 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,Y1,X1)| ~ product(Z2,Y2,X2)| equalish(X1,X2) ) ))),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f10,negated_conjecture,(
% 0.22/5.52 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,Y1,X1)| ~ product(Z2,Y2,X2)| equalish(Y1,Y2) ) ))),
% 0.22/5.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.52 fof(f11,plain,(
% 0.22/5.52 group_element(e_1)),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f1])).
% 0.22/5.52 fof(f12,plain,(
% 0.22/5.52 group_element(e_2)),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f2])).
% 0.22/5.52 fof(f13,plain,(
% 0.22/5.52 ~equalish(e_1,e_2)),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f3])).
% 0.22/5.52 fof(f15,plain,(
% 0.22/5.52 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2))),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f5])).
% 0.22/5.52 fof(f18,plain,(
% 0.22/5.52 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.22/5.52 inference(miniscoping,[status(thm)],[f7])).
% 0.22/5.52 fof(f19,plain,(
% 0.22/5.52 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f18])).
% 0.22/5.52 fof(f20,plain,(
% 0.22/5.52 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.22/5.52 inference(miniscoping,[status(thm)],[f8])).
% 0.22/5.52 fof(f21,plain,(
% 0.22/5.52 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f20])).
% 0.22/5.52 fof(f22,plain,(
% 0.22/5.52 ![X1,X2]: ((![Y2,Z2]: ((![Y1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,Y1,X1)))|~product(Z2,Y2,X2)))|equalish(X1,X2))),
% 0.22/5.52 inference(miniscoping,[status(thm)],[f9])).
% 0.22/5.52 fof(f23,plain,(
% 0.22/5.52 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X1,X0)|~product(X5,X4,X3)|equalish(X0,X3))),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f22])).
% 0.22/5.52 fof(f24,plain,(
% 0.22/5.52 ![Y1,Y2]: ((![X2,Z2]: ((![X1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,Y1,X1)))|~product(Z2,Y2,X2)))|equalish(Y1,Y2))),
% 0.22/5.52 inference(miniscoping,[status(thm)],[f10])).
% 0.22/5.52 fof(f25,plain,(
% 0.22/5.52 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X1,X0)|~product(X5,X4,X3)|equalish(X1,X4))),
% 0.22/5.52 inference(cnf_transformation,[status(thm)],[f24])).
% 0.22/5.52 fof(f26,plain,(
% 0.22/5.52 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.22/5.52 inference(resolution,[status(thm)],[f13,f21])).
% 0.22/5.52 fof(f27,plain,(
% 0.22/5.52 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.22/5.52 inference(resolution,[status(thm)],[f13,f19])).
% 0.22/5.52 fof(f29,plain,(
% 0.22/5.52 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.22/5.52 inference(resolution,[status(thm)],[f13,f25])).
% 0.22/5.52 fof(f30,plain,(
% 0.22/5.52 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_2,X2,X1)|~product(X3,X0,e_1)|~product(X3,X2,e_2))),
% 0.22/5.52 inference(resolution,[status(thm)],[f13,f23])).
% 0.22/5.52 fof(f36,plain,(
% 0.22/5.52 ![X0]: (~group_element(X0)|product(X0,e_2,e_1)|product(X0,e_2,e_2))),
% 0.22/5.52 inference(resolution,[status(thm)],[f15,f12])).
% 0.22/5.52 fof(f37,plain,(
% 0.22/5.52 ![X0]: (~group_element(X0)|product(X0,e_1,e_1)|product(X0,e_1,e_2))),
% 0.22/5.52 inference(resolution,[status(thm)],[f15,f11])).
% 0.22/5.52 fof(f38,plain,(
% 0.22/5.52 product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),
% 0.22/5.52 inference(resolution,[status(thm)],[f36,f12])).
% 0.22/5.52 fof(f39,plain,(
% 0.22/5.52 product(e_1,e_2,e_1)|product(e_1,e_2,e_2)),
% 0.22/5.52 inference(resolution,[status(thm)],[f36,f11])).
% 0.22/5.52 fof(f40,definition,(
% 0.22/5.52 sQ0_spl <=> (product(e_2,e_2,e_1))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f41,plain,(
% 0.22/5.52 product(e_2,e_2,e_1)|~sQ0_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f40])).
% 0.22/5.52 fof(f43,definition,(
% 0.22/5.52 sQ1_spl <=> (product(e_2,e_2,e_2))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f44,plain,(
% 0.22/5.52 product(e_2,e_2,e_2)|~sQ1_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f43])).
% 0.22/5.52 fof(f46,plain,(
% 0.22/5.52 sQ0_spl|sQ1_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f38,f40,f43])).
% 0.22/5.52 fof(f47,definition,(
% 0.22/5.52 sQ2_spl <=> (product(e_1,e_2,e_1))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f48,plain,(
% 0.22/5.52 product(e_1,e_2,e_1)|~sQ2_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f47])).
% 0.22/5.52 fof(f50,definition,(
% 0.22/5.52 sQ3_spl <=> (product(e_1,e_2,e_2))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f51,plain,(
% 0.22/5.52 product(e_1,e_2,e_2)|~sQ3_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f50])).
% 0.22/5.52 fof(f53,plain,(
% 0.22/5.52 sQ2_spl|sQ3_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f39,f47,f50])).
% 0.22/5.52 fof(f54,plain,(
% 0.22/5.52 ~product(e_2,e_2,e_1)|~sQ2_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f48,f26])).
% 0.22/5.52 fof(f56,plain,(
% 0.22/5.52 $false|~sQ0_spl|~sQ2_spl),
% 0.22/5.52 inference(forward_subsumption_resolution,[status(thm)],[f54,f41])).
% 0.22/5.52 fof(f57,plain,(
% 0.22/5.52 ~sQ0_spl|~sQ2_spl),
% 0.22/5.52 inference(contradiction_clause,[status(thm)],[f56])).
% 0.22/5.52 fof(f58,plain,(
% 0.22/5.52 ~product(e_2,e_2,e_2)|~sQ3_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f51,f26])).
% 0.22/5.52 fof(f59,plain,(
% 0.22/5.52 $false|~sQ1_spl|~sQ3_spl),
% 0.22/5.52 inference(forward_subsumption_resolution,[status(thm)],[f58,f44])).
% 0.22/5.52 fof(f60,plain,(
% 0.22/5.52 ~sQ1_spl|~sQ3_spl),
% 0.22/5.52 inference(contradiction_clause,[status(thm)],[f59])).
% 0.22/5.52 fof(f62,plain,(
% 0.22/5.52 ![X0,X1]: (~product(e_2,X0,e_2)|~product(X1,e_2,e_1)|~product(X1,X0,e_2)|~sQ3_spl)),
% 0.22/5.52 inference(resolution,[status(thm)],[f30,f51])).
% 0.22/5.52 fof(f63,plain,(
% 0.22/5.52 product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.22/5.52 inference(resolution,[status(thm)],[f37,f12])).
% 0.22/5.52 fof(f64,plain,(
% 0.22/5.52 product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),
% 0.22/5.52 inference(resolution,[status(thm)],[f37,f11])).
% 0.22/5.52 fof(f65,definition,(
% 0.22/5.52 sQ4_spl <=> (product(e_2,e_1,e_1))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f66,plain,(
% 0.22/5.52 product(e_2,e_1,e_1)|~sQ4_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f65])).
% 0.22/5.52 fof(f68,definition,(
% 0.22/5.52 sQ5_spl <=> (product(e_2,e_1,e_2))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f69,plain,(
% 0.22/5.52 product(e_2,e_1,e_2)|~sQ5_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f68])).
% 0.22/5.52 fof(f71,plain,(
% 0.22/5.52 sQ4_spl|sQ5_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f63,f65,f68])).
% 0.22/5.52 fof(f72,definition,(
% 0.22/5.52 sQ6_spl <=> (product(e_1,e_1,e_1))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f73,plain,(
% 0.22/5.52 product(e_1,e_1,e_1)|~sQ6_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f72])).
% 0.22/5.52 fof(f75,definition,(
% 0.22/5.52 sQ7_spl <=> (product(e_1,e_1,e_2))),
% 0.22/5.52 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.22/5.52 fof(f76,plain,(
% 0.22/5.52 product(e_1,e_1,e_2)|~sQ7_spl),
% 0.22/5.52 inference(component_clause,[status(thm)],[f75])).
% 0.22/5.52 fof(f78,plain,(
% 0.22/5.52 sQ6_spl|sQ7_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f64,f72,f75])).
% 0.22/5.52 fof(f80,plain,(
% 0.22/5.52 ~product(e_2,e_1,e_1)|~sQ6_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f73,f26])).
% 0.22/5.52 fof(f84,plain,(
% 0.22/5.52 $false|~sQ4_spl|~sQ6_spl),
% 0.22/5.52 inference(forward_subsumption_resolution,[status(thm)],[f80,f66])).
% 0.22/5.52 fof(f85,plain,(
% 0.22/5.52 ~sQ4_spl|~sQ6_spl),
% 0.22/5.52 inference(contradiction_clause,[status(thm)],[f84])).
% 0.22/5.52 fof(f86,plain,(
% 0.22/5.52 ![X0]: (~product(X0,e_2,e_1)|~product(X0,e_1,e_2)|~sQ5_spl|~sQ3_spl)),
% 0.22/5.52 inference(resolution,[status(thm)],[f69,f62])).
% 0.22/5.52 fof(f88,plain,(
% 0.22/5.52 ~product(e_2,e_2,e_2)|~sQ5_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f69,f27])).
% 0.22/5.52 fof(f89,plain,(
% 0.22/5.52 ~product(e_2,e_2,e_1)|~sQ3_spl|~sQ5_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f86,f69])).
% 0.22/5.52 fof(f90,plain,(
% 0.22/5.52 ~sQ0_spl|~sQ3_spl|~sQ5_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f89,f40,f50,f68])).
% 0.22/5.52 fof(f93,plain,(
% 0.22/5.52 ![X0,X1]: (~product(e_2,e_1,X0)|~product(X1,e_2,X0)|~product(e_1,e_2,X1)|~sQ7_spl)),
% 0.22/5.52 inference(resolution,[status(thm)],[f76,f29])).
% 0.22/5.52 fof(f94,plain,(
% 0.22/5.52 ~product(e_1,e_2,e_2)|~sQ7_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f76,f27])).
% 0.22/5.52 fof(f95,plain,(
% 0.22/5.52 $false|~sQ3_spl|~sQ7_spl),
% 0.22/5.52 inference(forward_subsumption_resolution,[status(thm)],[f94,f51])).
% 0.22/5.52 fof(f96,plain,(
% 0.22/5.52 ~sQ3_spl|~sQ7_spl),
% 0.22/5.52 inference(contradiction_clause,[status(thm)],[f95])).
% 0.22/5.52 fof(f100,plain,(
% 0.22/5.52 ![X0]: (~product(e_2,e_1,X0)|~product(e_1,e_2,X0)|~sQ2_spl|~sQ7_spl)),
% 0.22/5.52 inference(resolution,[status(thm)],[f48,f93])).
% 0.22/5.52 fof(f106,plain,(
% 0.22/5.52 ~product(e_2,e_1,e_1)|~sQ7_spl|~sQ2_spl),
% 0.22/5.52 inference(resolution,[status(thm)],[f100,f48])).
% 0.22/5.52 fof(f107,plain,(
% 0.22/5.52 ~sQ4_spl|~sQ7_spl|~sQ2_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f106,f65,f75,f47])).
% 0.22/5.52 fof(f110,plain,(
% 0.22/5.52 ~sQ1_spl|~sQ5_spl),
% 0.22/5.52 inference(split_clause,[status(thm)],[f88,f43,f68])).
% 0.22/5.52 fof(f112,plain,(
% 0.22/5.52 $false),
% 0.22/5.52 inference(sat_refutation,[status(thm)],[f46,f53,f57,f60,f71,f78,f85,f90,f96,f107,f110])).
% 0.22/5.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/5.59 % Elapsed time: 0.083435 seconds
% 0.22/5.59 % CPU time: 0.063916 seconds
% 0.22/5.59 % Total memory used: 1.157 MB
% 0.22/5.59 % Net memory used: 1.146 MB
%------------------------------------------------------------------------------